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A276627
Decimal expansion of K(3-2*sqrt(2)), where K is the complete elliptic integral of the first kind.
1
1, 5, 8, 2, 5, 5, 1, 7, 2, 7, 2, 2, 3, 7, 1, 5, 9, 1, 1, 8, 3, 3, 1, 3, 5, 0, 7, 1, 0, 7, 0, 4, 0, 9, 8, 7, 6, 5, 2, 9, 4, 8, 8, 1, 4, 9, 6, 1, 8, 7, 8, 9, 2, 4, 3, 4, 9, 7, 1, 6, 9, 4, 4, 8, 4, 7, 8, 2, 0, 8, 5, 3, 5, 1, 8, 6, 6, 6, 3, 5, 5, 1, 7, 3, 6, 2, 0, 9, 8, 1, 4, 0, 6, 5, 5, 4, 3, 2, 2, 2, 0, 0, 0, 4, 1
OFFSET
1,2
COMMENTS
The modulus k=3-2*sqrt(2).
K(k_4) in the Mathworld link.
LINKS
Eric Weisstein's World of Mathematics, Elliptic Integral Singular Values
I. J. Zucker and G. S. Joyce, Special values of the hypergeometric series II, Math. Proc. Camb. Phil. Soc. 131 (2001) 309-319. Table 1 N=4.
FORMULA
Equals 2*(2+sqrt(2))*Pi^(3/2)/Gamma(-1/4)^2.
Equals A174968 * A062539 /2. - R. J. Mathar, Aug 18 2023
Equals A093341 * A201488 [Zucker] - R. J. Mathar, Jun 24 2024
EXAMPLE
1.58255172722371591183313507107040987652948814961878924349716944847...
MAPLE
evalf(2*(2+sqrt(2))*Pi^(3/2)/GAMMA(-1/4)^2, 120); # Muniru A Asiru, Oct 08 2018
MATHEMATICA
RealDigits[N[EllipticK[(3 - 2 Sqrt[2])^2], 105]][[1]]
RealDigits[2*(2+Sqrt[2])*Pi^(3/2)/Gamma[-1/4]^2, 10, 100][[1]] (* G. C. Greubel, Oct 08 2018 *)
PROG
(PARI) default(realprecision, 100); 2*(2+sqrt(2))*Pi^(3/2)/gamma(-1/4)^2 \\ G. C. Greubel, Oct 08 2018
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); 2*(2+Sqrt(2))*Pi(R)^(3/2)/Gamma(-1/4)^2; // G. C. Greubel, Oct 08 2018
CROSSREFS
Cf. A157259 (for 3-2*sqrt(2)).
Sequence in context: A110989 A099736 A256453 * A119420 A134469 A238166
KEYWORD
nonn,cons
AUTHOR
STATUS
approved